Threads are machined in work pieces by thread forms mounted on threading bars. Typically, the thread forms are secured in removable threading cartridges. As the thread form wears, the thread form is ground and shaped, and then re-positioned on the threading cartridge using shims to ensure a constant height position of the cutting edge of the thread form on the threading bar. Imprecision in the position of the thread form can cause poor quality threading on the work piece. This invention is directed to an improved threading cartridge with a readily height adjustable thread form.